Errors in frequency response estimates using overlapping blocks with random inputs

Abstract Statistical errors in frequency response estimates depend on the form of the time window used to define data blocks. These errors are distributed along the individual blocks in a manner which is characteristic of the window used. A theory, valid for a wide range of systems and windows, is presented to derive this distribution. When overlapping blocks are used to reduce the variance of the estimates, the errors in adjacent blocks may contain both correlated and uncorrelated terms. The correlated terms may be of differing signs which reduces the sum of these terms and hence the variance of the final estimates. Simulation results are presented for both the rectangular (‘do nothing') window and the Hanning window and particular dynamic systems, chosen to demonstrate the salient results of the analysis.